Question;MAT540;Week;7 Homework;Chapter 3;8.;Solve the model;formulated in Problem 7 for Southern Sporting Goods Company using the computer.;a.;State the;optimal solution.;b.;What would;be the effect on the optimal solution if the profit for a basketball changed;from $12 to $13? What would be the effect;if the profit for a football changed from $16 to $15?;c.;What would;be the effect on the optimal solution if 500 additional pounds of rubber could;be obtained? What would be the effect if;500 additional square feet of leather could be obtained?;Reference Problem 7. Southern Sporting Good Company;makes basketballs and footballs. Each;product is produced from two resources rubber and leather. The resource requirements for each product;and the total resources available are as follows;Resource Requirements per Unit;Product;Rubber (lb.);Leather (ft2);Basketball;3;4;Football;2;5;Total resources available;500 lb.;800 ft2;10.;A company;produces two products, A and B, which have profits of $9 and $7;respectively. Each unit of product must;be processed on two assembly lines, where the required production times are as;follows;Hours/ Unit;Product;Line 1;Line2;A;12;4;B;4;8;Total Hours;60;40;a.;Formulate a;linear programming model to determine the optimal product mix that will;maximize profit.;b.;Transform;this model into standard form.;11.;Solve;problem 10 using the computer.;a.;State the;optimal solution.;b.;What would;be the effect on the optimal solution if the production time on line 1 was;reduced to 40 hours?;c.;What would be;the effect on the optimal solution if the profit for product B was increased;from $7 to $15 to $20?;12.;For the;linear programming model formulated in Problem 10 and solved in Problem 11.;a.;What are;the sensitivity ranges for the objective function coefficients?;b.;Determine;the shadow prices for additional hours of production time on line 1 and line 2;and indicate whether the company would prefer additional line 1 or line 2;hours.;14.;Solve the;model formulated in Problem 13 for Irwin Textile Mills.;a.;How much extra cotton and processing time are;left over at the optimal solution? Is;the demand for corduroy met?;b.;What is the;effect on the optimal solution if the profit per yard of denim is increased from;$2.25 to $3.00? What is the effect if;the profit per yard of corduroy is increased from $3.10 to $4.00?;c.;What would;be the effect on the optimal solution if Irwin Mils could obtain only 6,000;pounds of cotton per month?;Reference Problem 13. Irwin Textile Mills produces;two types of cotton cloth ? denim and corduroy.;Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5;pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton;per yard. A yard of corduroy requires;3.2 hours of processing time, a yard of denim requires 3.0 hours. Although the demand for denim is practically;unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6,500 pounds of cotton;and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.25 per;yard of denim and $3.10 per yard of corduroy.;The manufacturer wants to know how many yards of each type of cloth to;produce to maximize profit. Formulate;the model and put it into standard form.;Solve it.;15.;Continuing;the model from Problem 14.;a.;If Irwin;Mills can obtain additional cotton or processing time, but not both, which;should it select? How much? Explain your answer.;b.;Identify;the sensitivity ranges for the objective function coefficients and for the;constraint quantity values. Then explain;the sensitivity range for the demand for corduroy.;16.;United;Aluminum Company of Cincinnati produces three grades (high, medium, and low) of;aluminum at two mills. Each mill has a;different production capacity (in tons per day) for each grade as follows;Aluminum;Grade;Mill;1;2;High;6;2;Medium;2;2;Low;4;10;The company has contracted with a manufacturing;firm to supply at least 12 tons of high-grade aluminum, and 5 tons of low-grade;aluminum. It costs United $6,000 per day;to operate mill 1 and $7,000 per day to operate mill 2. The company wants to know the number of days;to operate each mill in order to meet the contract at minimum cost.;a.;Formulate a;linear programming model for this problem.;18.;Solve the;linear programming model formulated in Problem 16 for Unite Aluminum Company by;using the computer.;a.;Identify;and explain the shadow prices for each of the aluminum grade contract;requirements.;b.;Identify;the sensitivity ranges for the objective function coefficients and the;constraint quantity values.;c.;Would the;solution values change if the contract requirements for high-grade alumimum;were increased from 12 tons to 20 tons?;If yes, what would the new solution values be?;24.;Solve the;linear programming model developed in Problem 22 for the Burger Doodle;restaurant by using the computer.;a.;Identify;and explain the shadow prices for each of the resource constraints;b.;Which of the;resources constrains profit the most?;c.;Identify;the sensitivity ranges for the profit of a sausage biscuit and the amount of;sausage available. Explain these;sensitivity ranges.;Reference Problem 22. The manager of a Burger Doodle;franchise wants to determine how many sausage biscuits and ham biscuits to;prepare each morning for breakfast customers.;The two types of biscuits require the following resources;Biscuit;Labor;(hr.);Sausage;(lb.);Ham (lb.);Flour (lb.);Sausage;0.010;0.10;---;0.04;Ham;0.024;---;0.15;0.04;The franchise has 6;hours of labor available each morning.;The manager has a contract with a local grocer for 30 pounds of sausage;and 30 pounds of ham each morning. The;manager also purchases 16 pounds of flour.;The profit for a sausage biscuit is $0.60, the profit for a ham biscuit;is $0.50. The manager wants to know the;number of each type of biscuit to prepare each morning in order to maximize;profit. Formulate a linear programming;model for this problem.
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